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SageMath
E = EllipticCurve("id1")
E.isogeny_class()
Elliptic curves in class 176400id
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.tk1 | 176400id1 | \([0, 0, 0, -224175, 40878250]\) | \(-177953104/125\) | \(-875164500000000\) | \([]\) | \(1244160\) | \(1.8034\) | \(\Gamma_0(N)\)-optimal |
| 176400.tk2 | 176400id2 | \([0, 0, 0, 216825, 173619250]\) | \(161017136/1953125\) | \(-13674445312500000000\) | \([]\) | \(3732480\) | \(2.3527\) |
Rank
sage: E.rank()
The elliptic curves in class 176400id have rank \(1\).
Complex multiplication
The elliptic curves in class 176400id do not have complex multiplication.Modular form 176400.2.a.id
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
